Inferential signal generator for instrumented equipment and processes

ABSTRACT

Inferred sensor signals are generated for uninstrumented physical parameters not among parameters measured in processes and equipment having one or more sensors in place for monitoring physical parameters. Inferential sensor signals can be advantageously used in downstream control processing or analysis. The inferred sensor signals generated accordingly may be returned to a control system or display system local to the process or machine, or located at the remote location or yet a different remote location. The system can provide expected parameter values, as well as the differences between expected and input signals; or the system can provide raw measures of similarity between the collection of input signals and the collection of acceptable modeled states. A memory for storing the representative training set, or a transformation thereof, is coupled to a processor. The processor receives from an input data signals embodying real values from sensors and is disposed to acquire a complex signal to generate an estimate of one or more desired inferred sensors, using a linear combination of the representative training set sensor data.

FIELD OF THE INVENTION

The present invention relates to the monitoring of physical processesfor early detection of impending equipment failure or processdisturbance and on-line, continuous validation of sensor operation. Moreparticularly, the invention relates to systems and methods for thegeneration of replacement signals for failed sensors or for inferredsignals for physical parameters that are not directly instrumented.

BACKGROUND OF THE INVENTION

Monitoring the performance of almost any process (such as in refining,chemicals, steel, energy production) requires the use of sensors toassure that operation is maintained within prescribed constraints andthat equipment is performing within specifications to assure acceptableproduct quality and yield. Performance monitoring and optimization ofequipment and machines (automobile systems, jet engines, discretemanufacturing, etc.) similarly relies on sensors to ensure safeoperation and peak performance. A plethora of sensors have beendeveloped to measure electrical, thermal, chemical and physicalparameters of processes and equipment. Types of sensors includethermocouples, accelerometers, mass flow meters, acoustic sensors,stress and strain indicators, vibration sensors, and so on.

For most important process and equipment monitoring and controlapplications, sensors are nowadays electrically powered, and provide anelectrical indication (either analog or digital) of the parameter thatis sought to be measured. Furthermore, in many circumstances, sensorsare connected via a bus or network, and may contain sufficientprocessing power on-board to packetize sensor data and transmit itacross a network. In some cases, sensors are connected with or containwireless transmitters or transceivers for transmission of sensor data toa remote location.

Sensor data can be used in processes or in equipment operation in avariety of ways. Sensors provide validation that control settings havetaken effect, and a typical practice is to indicate an alarm when asensor reading exceeds or drops below a safety or tolerance threshold.Sensor data can also be streamed to a data repository for off-lineanalysis and trending, which is used to schedule maintenance or refine aprocess. A further use of sensor data is to provide feedback forcontinuous control of the operation of a process of piece of equipment.In an automobile engine, for example, a number of subsystems use sensordata to compute downstream settings for optimal engine performance, orto meet certain minimum clean air requirements.

There are a variety of circumstances in which it is difficult orimpossible to employ a sensor to measure a desired parameter. Theenvironment in which the sensor is placed may be hostile to thelongevity or even proper functioning of a sensor, as for example inmeasuring the flow of a gas containing a problematically highconcentration of corrosive acid. Alternatively, the environment mayrequire a sensor that is prohibitively expensive or hard to come by. Inanother alternative circumstance, the measurement sought may beimpossible to reasonably measure directly, as in attempting to determinethe remaining empty volume of an unusually shaped chamber partiallyfilled with a liquid. In yet other circumstances, the deployment of asensor may adversely weaken or otherwise impact the process or systembeing monitored. For example, in a closed fluid system such as ahydraulic system, placement of a sensor through the wall of the systemto directly measure a property of the fluid presents a point of weaknessand potential failure in the closed system. What is needed is a way ofindirectly measuring the parameter in question.

Under such circumstances, one may attempt to measure one or more otherparameters in order to infer the desired parameter. This may requireoutfitting the process or equipment with additional sensors, and usingcomputing resources to compute the inferred parameter. However, it isgenerally difficult to successfully do this. Furthermore, it usuallyrequires a great deal of study and knowledge of the process orequipment, or an understanding of the “first-principles” dynamics of thesystem, which may not be readily obtained without an unreasonable amountof research time and cost. What is needed is an effective way ofinferring a hard-to-measure parameter from other measured parameters ofa system that correlate in some way, without requiring a completeknowledge of the dynamics of the system and the parameters involved.

Such a need also exists for the circumstance of manufacturing aninstrumented product, such as an engine or other machine, which usessensors for feedback control, safety, or performance optimization. It ishighly desirable to reduce the cost of producing the product by notoutfitting the product with a sensor for every parameter, but insteadinferring some parameters based on readings from other sensors. Such aninference may be possible using a subset of sensors for the machine orengine, coupled with extensive knowledge of the behavior of all theparameters in tandem. However, the requisite knowledge can be difficultand costly to develop. Furthermore, the cost of additional computingpower that may be required on-board the product to calculate theinferred sensor values may outweigh the cost savings of removing sensorsin the first place. What is needed is a computationally efficient way ofinferring values for sensors “removed” from the production units fromvalues of sensors that are in fact built into the production units ofthe product.

An additional difficulty is presented with the failure of sensors. As anexample, sensors may be used to monitor a process or equipment to detectwhen it deviates from “normal” or correct operation. Normal can mean anacceptable functioning state, or it can be the most preferred of a setof various acceptable states. However, in practice the deviation can bedue to a change in the underlying parameter measured by the sensor, orto a faulty sensor. Hence, it is essential that the health of thesesensors is also known, and disturbances initiated by sensor faultsshould be identified and differentiated from process deviations. Often,even though a sensor has failed, it is desirable to continue processoperation and the failed sensor must be replaced with a replacement or“virtual” sensor providing the same information. What is needed is a wayof providing an output or estimate for a failed sensor within a systemto enable continued operation.

“First principles” techniques are known in the art for generating“virtual” sensor data based on other real sensor data. Maloney et al.describe in “Pneumatic And Thermal State Estimators For ProductionEngine Control And Diagnostics”, Electronic Engine Controls 1998,estimator algorithms implemented in a production grade speed-densityEngine Management Systems (EMS). A critical and basic need in the designof EMS control and diagnostic algorithms is the availability ofinformation describing the state of the engine. The estimator algorithmsprovide engine mass flow, pressure, and temperature estimates forgeneral use by control, diagnostic, and other estimator algorithms.Maloney et al. describe the development of such first principles modelswith fully instrumented engines in the laboratory, to compute virtualsignals off of real sensor signals. The development is involved andhighly specific to the application presented. It would thus be desirableto provide a general method for the generation of missing values orvirtual signals without have to resort to developing first principlesmodels.

In a related trend, processes or machines are monitored bysoftware-based systems that monitor correlated sensor values inaggregate. Such a system is described in U.S. Pat. No. 5,764,509 toGross et al., the teachings of which are hereby incorporated byreference. Such a system for monitoring or providing control over aprocess or machine is superior to traditional threshold-typesensor-based monitoring and control because it can generallydifferentiate the normal or acceptable behavior of the process ormachine from unacceptable or alarm states long before the thresholdsystem. Gross et al. teach an empirical modeling technique that acceptsas inputs a set of current sensor readings for linearly and non-linearlycorrelated parameters of the monitored process or machine, and generatesestimates as outputs of what those current sensor readings ought to be.This is then compared using a statistical hypothesis test for eachsensor to determine whether any sensor is showing a statisticallysignificant deviation from what is expected. The empirical model ofGross et al. is created from a history of collected data representingthe expected ranges of operation for the monitored process or machine.

An important issue for such a system is the robustness of the systemwhen presented with a failure of a sensor, as opposed to a process orfunctional deviation. A bad sensor signal input to such a systempotentially can impact the estimates made by the model for all thesensors in the process or machine. Furthermore, other control modulesoutside the monitoring system may be relying on the bad sensor signal.It would be beneficial in such systems to reduce the impact of a failedsensor on the ability of the system to generate accurate estimates andtherefore accurately portray the operational state of the process ormachine. It would be additionally advantageous to be able to generate areplacement signal for the failed sensor and make it available to anyother control systems that normally rely on raw real-time sensorsignals. There is a need for a way to handle a bad sensor under thesecircumstances in an empirical modeling system like that by Gross et al.

SUMMARY OF THE INVENTION

The present invention provides an improved system and method forproducing replacement sensor signals for failed sensors, and inferredsensor signals for non-instrumented physical parameters, in processesand equipment having one or more sensors in place for monitoringphysical parameters. The system can provide expected parameter values,as well as the differences between expected and input signals; or thesystem can provide raw measures of similarity between the collection ofinput signals and the collection of acceptable modeled states.

In a process or machine that is fully instrumented with sensors for allparameters of interest, sensor data is collected for all regimes ofexpected later operation of the same or similar processes or machines.This collected data forms a history from which the inventive system can“learn” the desired or normal operation of the process or machine, usingtraining routines that distill it to a representative set of sensordata. Using this representative training set of sensor data, thedescribed embodiments monitor the process or machine in real-timeoperation (or in batch mode, if preferred), and generate estimates forcertain of the sensors for which historic data was collected, but whichhave failed or which were removed from the process or machine. Theinvention can be employed as a safeguard that is triggered to produce areplacement sensor signal when an actual sensor fails (anautoassociative or replacement mode). It can also be used to produce aninferred sensor signal to reduce the production cost of a machine byreducing the number of sensors that are needed to monitor and controlthe machine (an inferential mode).

The apparatus of the present invention can be deployed as anelectrically powered device with memory and a processor, physicallylocated on or near the process or machine for which the “virtual” signalis generated. Alternatively, it can be located remotely from the processor machine, as a module in a computer receiving sensor data from livesensors on the process or machine via a network or wireless transmissionfacility. The replacement or inferred sensor signals generatedaccordingly may be returned to a control system or display system localto the process or machine, or located at the remote location or yet adifferent remote location.

A memory for storing the representative training set, or atransformation thereof, is coupled to a processor. The processorreceives from an input data signals embodying real values from sensorsactually on the process or machine, and may receive these in real-time.The processor is disposed to take a set of readings of the actualsensors from the input, and generate an estimate of one or more desiredinferred sensors, using a linear combination of the representativetraining set sensor data, as weighted by the result of a measure ofsimilarity of the input sensor data to the representative training setsensor data.

Accordingly, it would be advantageous to provide a method of generatingan estimate of a physical parameter of a process or machine based onsensor values for other physical parameters of the process or machine,and based on a set of sensor data for the process or machinerepresentative of past operation. The improved monitoring system mayaccept an input set of sensor data for a process or machine, and provideas output at least one estimate of a parameter of the process or machinethat is not among the sensor inputs. A computationally efficient methodand apparatus for generating a replacement signal for a parameter in asensor-monitored process or machine is also desirable when it isdetermined that a sensor has failed. To this end, it would beadvantageous to provide a computer-executable module for generating areplacement sensor signal for a failed sensor, or an inferred sensorsignal for a non-instrumented parameter, based on an input of otherparameters or a process or machine, and for outputting the estimate to adisplay or control system. A microprocessor-based component may be addedto a machine to interface with sensor data in the machine to provideinferred estimates of at least one additional physical parameter of themachine not measured by sensors.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features believed characteristic of the invention are setforth in the appended claims. The invention itself, however, as well asthe preferred mode of use, further objectives and advantages thereof, isbest understood by reference to the following detailed description ofthe embodiments in conjunction with the accompanying drawings, wherein:

FIG. 1 illustrates steps for setting up inventive virtual signalgeneration for a process or machine;

FIG. 2 illustrates a method for creating a representative “training”data set from collected sensor data for use in the invention;

FIG. 3 illustrates a flowchart for creating a representative “training”data set from collected sensor data for use in the invention;

FIG. 4 is a diagram of an arrangement for obtaining a data set historyfor a machine, for use in the present invention;

FIG. 5 illustrates an on-board processor embodiment of the presentinvention for generating virtual signals for a monitored or controlledmachine or process;

FIG. 6 illustrates a remote monitoring embodiment of the presentinvention for generating virtual signals for a monitored or controlledmachine or process;

FIG. 7 illustrates a flowchart for generating a set of one or morevirtual sensor signals according to the present invention;

FIG. 8 illustrates the computation of one of the similarity operators ofthe present invention;

FIG. 9 illustrates a flowchart of decision logic for generating areplacement virtual signal in a monitored process or machine accordingto the invention;

FIG. 10 illustrates a hydraulic system capable of being monitored bywith the present invention using a complex signal; and

FIG. 11 shows a chart of a virtual signal generated as compared to thecorresponding actual sensor signal in accordance with the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Turning to FIG. 1, a flowchart generally shows the steps for setting upand using a process, machine, system or other piece of equipment,whether mechanical, electrical or biological in accordance with theinvention. In step 110, a described embodiment of the process or machinefrom which inferred or replacement signals may be generated inoperation, is fully instrumented with sufficient sensors to measure allparameters of interest, including the parameters for which virtualsignals will be generated. In step 120, sensor data is collected as theprototype is operated through all ranges of operation that are expectedlater. In step 130, one of several “training” methods is used to distillthe sensor data collected in step 120 into a subset sufficient torepresentative the operational ranges and correlations between thesensors over those ranges. These methods will be discussed below. Instep 140, the distilled representative sensor data or a transformationof that data, including data elements corresponding to each of the (all)sensors with which the prototype was instrumented, is loaded into aprocessor memory that will provide for generation of virtual sensorsignals for the process or machine in normal operation. In step 150, theapplication for generating virtual sensor signals is as replacementsensor signals for sensors that fail in operation. In step 160, theapplication for generating virtual sensor signals is as inferred signalsfor sensors that are removed or not built into production runs of likemachines or equipment, thus saving the cost of the absent sensors whilenonetheless providing signals for downstream processing.

The described embodiments substantially provide the process or machinefor which virtual signals will be generated in operation. For example,in the case of an engine, a prototype engine can be fully instrumentedin a laboratory bench setting with sensors for all parameters. Theprototype engine is then operated through a variety of operationalranges, and sensor data for all the sensors is recorded, usually asdigitized and time-stamped values by means of digital computers attachedto and in communication with the sensor outputs. Using the computerprocessor and software of the described embodiments, the collectedsensor data is then distilled down to a subset of sensor data thatrepresents the operational ranges for which data was collected. Wherethe goal is to mass produce this engine with a reduced cost ofproduction by building in fewer sensors, but still have all the sensorsignals available for engine monitoring and control, the distilledrepresentative data is provided in an inventive computer software moduleand processor hardware for executing it, that can be built into theengine monitoring or control system, and that generates virtual signalsfor the missing sensors as detailed below. The system described in thepreferred embodiments provides for monitoring of the instrumentedequipment with a plurality of sensors capable of being monitored with aninformation processor. A data acquisition input front end is providedfor use with the information processor for receiving operational valuesdescriptive of physical parameters of the system. Time-correlated sensordata representative of expected operational states and signals observedfrom the instrumented equipment during operation are used by theinformation processor for generating outputs that are descriptive of aparameter that may include or be provided in addition to signalsobserved from the instrumented equipment. The information processor isoperable in response to the plurality of sensors of the instrumentedequipment for establishing relationships between the component signalsand one or more process parameters of the equipment to generate one ormore parametric signals corresponding to process parameters of thesystem.

As another example, for a process in which it is desirable to measure aparameter that would require placing a sensor in a corrosive ordestructive environment, a mock-up of the process can be constructed ina laboratory setting, fully instrumented. The mock-up can be operatedthrough the expected ranges of later operation, and data collected overthese ranges. While one or more sensors may eventually be destroyed thisway until enough data is collected, the subsequent inventive inferentialmodel will enable full-scale operation of the process in questionwithout any subsequent need to replace further destroyed sensors. Theparameter can be generated in operation by the computer module of thedescribed embodiments, referencing the representative data distilledfrom data collected in the laboratory.

The amount of historic data that must be collected to provide for therepresentative training set is of course contingent on the specificapplication and the variety of operational modes and ranges that will beencountered in normal monitored operation, but in any case usuallyrepresents much less time and effort than is required to study thesystem through all its ranges to derive a first-principles model of thesystem. Importantly, the data collected should include both sides of anyhysteresis present in the operational modes.

The described embodiments thus provide an extremely beneficial empiricalapproach to providing replacement sensor signals or inferred sensorsignals for process or machine monitoring or control. It avoids thelengthy or perhaps insurmountable task of developing a first-principlesmodel and understanding of the relationships between all theinstrumented parameters.

Turning to FIG. 2, a method for step 130 is graphically depicted fordistilling the collected sensor data from step 120 to create arepresentative training data set. Five sensor signals 202, 204, 206, 208and 210 are shown for a process or machine in which later one or more ofthe five will be inferentially generated. The abscissa axis 215 is thesample number or time stamp of the collected sensor data, where the datais digitally sampled and the sensor data is temporally correlated. Theordinate axis 220 represents the relative magnitude of each sensorreading over the samples or “snapshots”. Each snapshot represents avector of five elements, one reading for each sensor in that snapshot.Of all the sensor data collected in step 120 (all the snapshots),according to this training method, only those five-element snapshots areincluded in the representative training set that contain either a globalminimum or a global maximum value for any given sensor. Therefore, forsensor 202, the global maximum 225 justifies the inclusion of the fivesensor values at the intersections of line 230 with each sensor signal,including global maximum 225, in the representative training set, as avector of five elements. Similarly, for sensor 202, the global minimum235 justifies the inclusion of the five sensor values at theintersections of line 240 with each sensor signal.

Selection of representative data is further depicted in FIG. 3. Datacollected in step 130 has N sensors and L observations or snapshots ortemporally related sets of sensor data that comprise an array X of Nrows and L columns. In step 304, a counter i for element number isinitialized to zero, and an observation or snapshot counter t isinitialized to one. Two arrays “max” and “min” for containing maximumand minimum values respectively across the collected data for eachsensor, are initialized to be vectors each of N elements which are setequal to the first column of X. Two additional arrays Tmax and Tmin forholding the observation number of the maximum and minimum value seen inthe collected data for each sensor, are initialized to be vectors eachof N elements, all zero.

In step 307, if the sensor value of sensor i at snapshot t in X isgreater than the maximum yet seen for that sensor in the collected data,max(i) is update to equal the sensor value and Tmax(i) stores the numbert of the observation in step 310. If not, a similar test is done for theminimum for that sensor in steps 314 and 317. The observation counter tis incremented in step 320. In step 322, if all the observations havebeen reviewed for a given sensor (t=L), then t is reset and i isincremented (to find the maximum and minimum for the next sensor) instep 325. If the last sensor has been finished (i=N), step 328, thenredundancies are removed and an array D is created from a subset ofvectors from X.

First, in step 330, counters i and j are initialized to one. In step333, the arrays Tmax and Tmin are concatenated to form a single vectorTtmp having 2N elements. These elements are sorted into ascending (ordescending) order in step 336 to form array T. In step 339, holder tmpis set to the first value in T (an observation number that contains asensor minimum or maximum). The first column of D is set equal to thecolumn of X corresponding to the observation number that is the firstelement of T. In the loop starting with decision step 341, the ithelement of T is compared to the value of tmp that contains the previouselement of T. If they are equal (the corresponding observation vector isa minimum or maximum for more than one sensor), it has already beenincluded in D and need not be included again. Counter i is incrementedin step 350. If they are not equal, D is updated to include the columnfrom X that corresponds to the observation number of T(i) in step 344,and tmp is updated with the value at T(i). The counter j is thenincremented in step 347. In step 352, if all the elements of T have beenchecked, then the distillation into training set D has finished, step355.

Turning to FIG. 4, a schematic diagram of a laboratory workbencharrangement is shown for gathering process or machine behavior data fordistillation. A machine prototype 410 is depicted, which may be any kindof machine for which virtual sensors are required or desirable. Forexample, machine 410 may be a combustion engine, an electric motor, apump, a compressor, a refrigerator, and so on. The machine 410 is calleda prototype, but importantly, it should generate sensor data that issubstantially the same as the actual parameter values expected in aproduction model of the machine, as would be measured by the samesensors. Of course, the prototype may also be an instance of theproduction model itself, and ideally need not differ in any way fromother production models. The machine 410 may be connected to andcontrolled by a control system 420, generally comprising amicrocontroller- or microprocessor-based digital system with appropriateanalog/digital and digital/analog inputs and outputs as necessary.Machine 410 is instrumented with sensors that provide sensor valuesalong outputs 430. While all parameters of interest are instrumented inthis laboratory workbench arrangement, it is understood that only asubset 440 of the sensors will be employed in a production model of themachine 410, while a second subset 450 of sensors will not be employedor cannot be reliably employed in the production model of the machine410. This may be done to avoid costs for sensors 450, or may be due tothe difficulty or impossibility of employing sensors 450 for as long asneeded in the production model. The machine 410 is operated through theexpected range of operations, and data acquisition system 460 may beused to then record the values of all sensors 430 with which machine 410is instrumented. Additionally, control signals from control system 420may also be recorded by data acquisition system 460, and may be used as“sensor signals” that correlate with the other sensor signals.

Data acquired by data acquisition system 460 can accordingly beprocessed using a computer module 480 for producing a distilled trainingset of data representing the operational ranges of machine 410, usingthe training method described above, or other methods as may be known inthe art.

In the presently described embodiment an on-board processor is shown inFIG. 5, wherein a machine (or process) 508 is controlled by a controlsystem 517 that is located on the machine. Machine 508 is instrumentedwith sensors for some of the physical or logical parameters of interestin controlling the machine, and the outputs for these sensors are shownas output conductors 523, which feed into the control system 517. Theseare also feed to a processor 545 located within or on the machine,disposed to execute a computing program for generating a set 530 of atleast one virtual signal from the signals on the output conductors 523.The processor is connected to a memory 551, also on or in the machine,which stores data comprising the training set distilled to represent theexpected operational states of the machine 508. Memory 551 can alsoadvantageously store programs for execution by the processor 545. Thevirtual signals 530 generated by the processor 545 are provided to thecontrol system 517, in lieu of genuine sensor values for physical orlogical parameters of the machine. In this way, using a processor andmemory located on or within the machine, the control system for themachine can advantageously be provided with sufficient physicalparameter values of the machine to effectively control it, even if someof the physical parameters have not been instrumented, due to costsavings considerations, or due to the impracticability of instrumentingone or more physical parameters.

Processor 545 can also be a part of the control system 517, and in factcan be the processor on which the control system routines are executed,in the event the control system is a digital computed control system.Ideally, the processor 545 and memory 551 are powered by the same powersource as the control system. However, under certain circumstances, itmay also be preferable to provide for a processor and memory independentfrom the processor and/or memory of the control system, in order toprovide virtual signals 530 in a timely fashion, as though they weretruly instrumented parameters. For example, it may be necessary thatprocessor 545 must operate at a higher clock speed than any processoravailable within the control system, in order to provide virtual signalsin a way that appears to the control system indistinguishable from agenuinely instrumented parameter. Also, processor 545 and memory 551 cancomprise a separate unit from the control system with its own powersupply that can be retrofitted to an existing machine and controlsystem.

According to another embodiment, a process 603 is shown in FIG. 6 to beinstrumented with sensors having output leads 606. These provide sensorsignals to a control system 610 that controls the process. These signalsare also provided to a remote communications link 613, which is disposedto communicate digital values of the sensor signals to a second remotecommunications link 615, located at a physically remote place. Aprocessor 618 is provided, which may comprise a computing system andsoftware, that uses the sensor signals received by link 615 to generateat least one virtual sensor signal indicative of an inferred physicalparameter of process 603. A memory 620 is provided to store training setdata representative of the expected operational behavior of the process603, according to the distillation method described above. Furthermore,a display 623 may be provided at the remote location for displaying datadescriptive of the process 603, comprising sensor signals 606 or thevirtual signals derived therefrom or both. The virtual signals generatedby processor 618 can also be transmitted from link 615 back to link 613and input over leads 627 to control system 610 for advantageous controlof the process. Data comprising original sensor signals and/or virtualsensor signals can also be transmitted to a third remote communicationslink 630, located at yet a third distant place, for display on display633, thereby providing valuable information concerning the process tointerested parties located at neither the physical plant of the processnor at the site of computing the virtual signals.

The remote communications links can be selected from a variety oftechniques known in the art, including internet protocol based packetcommunication over the public telecommunications infrastructure, directpoint-to-point leased-line communications, wireless or satellite. Morespecifically, remote links 613, 615 and 630 may be internet-enabledservers with application software for accumulating, queuing andtransmitting data as messages, and queues for receiving andreconstituting data arriving as messages. Alternatively, communicationscan be synchronous (meaning in contrast to asynchronous, message-basedcommunications) over a wireless link.

The embodiment of the invention shown in FIG. 6 provides computation ofthe virtual signals using computing resources that are locatedgeographically distant from the process (or machine) being monitoredand/or controlled with the virtual signals. One benefit of this is thatthe computing resources for generating the virtual signals may be sharedfor a multitude of processes or machines, where the memory 620 may holdmultiple sets of training sets of data characterizing the variousmonitored processes and machines. Another benefit is that the virtualsignal results may be displayed and also potentially used in furtheranalysis by interested parties located distant from the process beingmonitored.

The calculations to be carried out by the information processor aredescribed in detail below. Using as an example a machine that will bemass produced that has fifteen total physical parameters of interest, weassume ten of these will be instrumented with real sensors providingreal signals during machine operation, and five signals will be inferredfrom the first ten, thereby reducing the cost to produce the machine bythe cost of the sensors for these five parameters. In what follows, thesubscript “in” generally corresponds to the ten real sensors whosevalues are input to the calculations, and the subscript “out” generallycorresponds to the five inferred sensor values that are output by thecalculation.

The step of providing a representative training set according to thedescription above results in a matrix D of values, having fifteen rows(corresponding to all fifteen parameters measured in the test or labsetting) and a sufficient number n of columns (sets of simultaneous ortemporally related sensor readings) to properly represent the fullexpected dynamic operating range of the machine. The matrix D comprisestwo adjoined matrices, D_(in) and D_(out), each having n columns: D_(in)has ten rows (corresponding to the ten real sensors) and D_(out) hasfive rows, corresponding to the five inferred sensors. While the orderof the columns does not matter in D, the ith column in both D_(in) andD_(out) must correspond.

Then, using y_(in) to designate a vector having ten elementscorresponding to the values of the ten real sensors (preferably inreal-time), a vector y_(out) is generated having five elementscorresponding to the five inferred sensor values, according to:

{right arrow over (y)} _(out) ={overscore (D)} _(out) ·{right arrow over(W)}

where W is a weight vector having as many elements N as there arecolumns in D, generated by:$\overset{\rightarrow}{W} = \frac{\underset{\rightarrow}{\hat{W}}}{\left( {\sum\limits_{j = 1}^{N}{\hat{W}(j)}} \right)}$$\hat{\underset{\rightarrow}{W}} = {\left( {{\overset{\_}{D}}_{in}^{T} \otimes {\overset{\_}{D}}_{in}} \right)^{- 1} \cdot \left( {{\overset{\_}{D}}_{in}^{T} \otimes {\overset{\rightarrow}{y}}_{in}} \right)}$

where represents a similarity operation between the two operandsdescribed in greater detail below that yeilds an array. The superscript“T” here represents the transpose of the matrix, and superscript “−1”represents the inverse of the matrix of resulting array. Importantly,there must be row correspondence to same sensors for the rows in D_(in)and y_(in), and for D_(out) and y_(out). That is, if the first row ofthe representative training set matrix D_(in) corresponds to values fora first sensor on the machine, the first element of y_(in) must also bethe current value (if opeating in real-time) of that same first sensor.

Turning to FIG. 7, the generation of one or more replacement or inferredsignals is shown in a flowchart. The flowchart shows the generation ofone replacement or inferred signal in the described embodiments, provideinput of one snapshot of actual sensors values in real-time operation.Matrix D_(in) is provided in step 705, along with the input snapshotvector y_(in) and an array A for computations. A counter i isinitialized to one in step 708, and is. used to count the number ofobservations in the training matrix D_(in). In step 712, another counterk is initialized to one (used to count through the number of sensors ina snapshot and observation), and array A is initialized to containzeroes for elements.

In step 715, the element-to-element similarity operation is performedbetween the kth element of y_(in) and the (ith, kth) element in D_(in).These elements are corresponding sensor values, one from actual input,and one from an observation in the training history D_(in). Thesimilarity operation returns a measure of similarity of the two values,usually a value between zero (no similarity) and one (identical) whichis assigned to the temporary variable r. In step 720, r divided by thenumber of sensors M is added to the ith value in the one-dimensionalarray A. Thus, the ith element in A holds the average similarity for theelemental similarities of y_(in) to the ith observation in D_(in). Instep 724, counter k is incremented.

In step 729, if all the sensors in a particular observation in D_(in)have been compared to corresponding elements of y_(in), then k will nowbe greater than M, and i can be incremented in step 731. If not, thenthe next element in y_(in) is compared for similarity to itscorresponding element in D_(in).

When all the elements of the current actual snapshot y_(in) have beencompared to all elements of an observation in D_(in), a test is made instep 735 whether this is the last of the observations in D_(in). If so,then counter i is now more than the number of observations N in D_(in),and processing moves to step 738. Otherwise, it moves back to step 712,where the array A is reset to zeroes, and the element (sensor) counter kis reset to one. In step 738, a weight vector W-carrot is computed fromthe equation shown therein, where represents a similarity operation,typically the same similarity operator as is used in step 715. In step743 W-carrot is normalized using a sum of all the weight elements inW-carrot, which ameliorates the effects in subsequent steps of anyparticularly large elements in W-carrot, producing normalized weightvector W. In step 746, this is used to produce the replacement orinferential output y_(out) using D_(out) . The output vector may havejust one element, in the case that only one replacement or inferentialsignal is being generated, or it may have multiple elements,corresponding to each “virtual” sensor being generated. The matrixD_(out) has been described above as containing counterpart training datafor the sensor(s) being generated.

The similarity operation can be selected from a variety of knownoperators that produce a measure of the similarity or numericalcloseness of rows of the first operand to columns of the second operand.The result of the operation is a matrix wherein the element of the ithrow and jth column is determined from the ith row of the first operandand the jth column of the second operand. The resulting element (i,j) isa measure of the sameness of these two vectors. In the describedembodiment, the ith row of the first operand generally has elementscorresponding to sensor values for a given temporally related state ofthe machine, and the same is true for the jth column of the secondoperand. Effectively, the resulting array of similarity measurementsrepresents the similarity of each state vector in one operand to eachstate vector in the other operand.

By way of example, one similarity operator that can be used compares thetwo vectors (the ith row and jth column) on an element-by-element basis.Only corresponding elements are compared, e.g., element (i,m) withelement (j,m) but not element (i,m) with element (j,n). For each suchcomparison, the similarity is equal to the absolute value of the smallerof the two values divided by the larger of the two values. Hence, if thevalues are identical, the similarity is equal to one, and if the valuesare grossly unequal, the similarity approaches zero. When all theelemental similarities are computed, the overall similarity of the twovectors is equal to the average of the elemental similarities. Adifferent statistical combination of the elemental similarities can alsobe used in place of averaging, e.g., median.

Another example of a similarity operator that can be used can beunderstood with reference to FIG. 8. With respect to this similarityoperator, the teachings of U.S. Pat. No. 5,987,399 to Wegerich et al.are relevant, and are incorporated in their entirety by reference. Foreach sensor or physical parameter, a triangle 804 is formed to determinethe similarity between two values for that sensor or parameter. The base807 of the triangle is set to a length equal to the difference betweenthe minimum value 812 observed for that sensor in the entire trainingset, and the maximum value 815 observed for that sensor across theentire training set. An angle Ω is formed above that base 807 to createthe triangle 804. The similarity between any two elements in avector-to-vector operation is then found by plotting the locations ofthe values of the two elements, depicted as X₀ and X₁ in the figure,along the base 807, using at one end the value of the minimum 812 and atthe other end the value of the maximum 815 to scale the base 807. Linesegments 821 and 825 drawn to the locations of X₀ and X₁ on the base 807form an angle θ. The ratio of angle θ to angle Ω gives a measure of thedifference between X₀ and X₁ over the range of values in the trainingset for the sensor in question. Subtracting this ratio, or somealgorithmically modified version of it, from the value of one yields anumber between zero and one that is the measure of the similarity of X₀and X₁.

Any angle size less than 180 degrees and any location for the angleabove the base 807 can be selected for purposes of creating asimilarity, but whatever is chosen must be used for all similaritymeasurements corresponding to particular sensor and physical parameterof the process or machine. Thus, differently shaped triangles 804 can beused for different sensors. One method of selecting the overall shape ofthe triangle is to empirically test what shape results in consistentlymost accurate virtual signal results.

For computational efficiency, angle Ω can be made a right angle (notdepicted in the figure). Designating line segment 831 as a height h ofthe angle Ω above the base 807, then angle θ for a givenelement-to-element similarity for element i is given by:$\theta_{i} = {{\tan^{- 1}\left( \frac{h}{X_{1}(i)} \right)} - {\tan^{- 1}\left( \frac{h}{X_{0}(i)} \right)}}$

Then, the elemental similarity is:$s_{i} = {1 - \frac{\theta_{i}}{\pi/2}}$

As indicated above, the elemental similarities can be statisticallyaveraged or otherwise statistically treated to generate an overallsimilarity of a snapshot to another snapshot, as if called for by thesystem.

Yet another class of similarity operator that can be used in thedescribed embodiments involves describing the proximity of one statevector to another state vector in n-space, where n is the dimensionalityof the state vector of the current snapshot of the monitored process ormachine. If the proximity is comparatively close, the similarity of thetwo state vectors is high, whereas if the proximity is distant or large,the similarity diminishes, ultimately vanishingly. By way of example,Euclidean distance between two state vectors can be used to determinesimilarity. In a process instrumented with 20 sensors, for example,wherein a 21^(st) uninstrumented parameter is beneficially inferred, theEuclidean distance between the currently monitored snapshot, comprisinga 20 element state vector, and each state vector in the training set(comprising a 20 element vector where the 21^(st) element correspondingto the virtual sensor has been left out) provides a measure ofsimilarity, as shown:$S = \frac{1}{\left\lbrack {1 + \frac{{{\overset{\rightarrow}{x} - \overset{\rightarrow}{d}}}^{\lambda}}{c}} \right\rbrack}$

wherein X is the current snapshot, and d is a state vector from thetraining set, and λ and c are user-selectable constants.

Turning to FIG. 9, decision logic is depicted for a method of checkingfor failed sensors and generating replacement signals in responsethereto according to the invention. Such a method can be embodied in aprocessor and memory as would be known in those skilled in the art, toprovide a system for monitoring a machine or process in real-time andgenerating one or more replacement virtual signals as necessary inresponse to a detected failure of a sensor on the machine or process. Instep 903, a FLAG variable is initialized to zero, and a snapshot countert is also initialized to zero. On the first loop through the method, ift is zero in step 906, then initial training is carried out in step 908.A training set 912 distilled in the described embodiment provides atraining matrix of snapshots 917. In step 908, the matrix D_(in) andD_(out) are set equal to matrix D of 917, the FLAG is set to zero, t isset to 1 and an intermediate matrix G₀ is found by:

G ₀ ⁻¹=(D _(in) ₀ ^(T) {circle around (X)}D _(in) ₀ )⁻¹

using the similarity operation.

Real-time or on-line monitoring of the machine or process by acquisitionof real sensor data 920 then proceeds in step 922, wherein a snapshotX_(t) of time-correlated or coincident data is acquired from sensors onthe machine or process. The acquired data is used to compute estimatedvalues for all the sensors according to:

{circumflex over (X)} _(t) =D _(out) ·G _(t) ⁻¹·(D _(in) _(t) ^(T){circle around (X)}X _(t))

Such an estimate of all the sensors has utility as is known in the priorart, such as Gross et al. mentioned above, for comparing to the realsensor values and detecting when a process change is occurring. As caneasily be discerned from this figure, if no sensors on the monitoredmachine or process have failed, then the matrices D_(out) and D_(in)(0)are equivalent.

A decision engine in step 926 examines whether any sensors have failed.Any of a variety of techniques known in the prior art for detectingsensor failure can be used, and can work by examining just the originalmonitored data or by comparing the monitored data to the estimated data.By way of example, one technique for determining whether a sensor hasfailed is to monitor whether the reading from the sensor has frozen at asingle value over a sequence of readings over which it should havechanged. As another example, sensor failure can be determined when asensor reading suffers a sharp discontinuity or drops to zero,especially when the physical parameter being measured by the sensorcannot possibly be zero. In addition, certain “smart” sensors areavailable commercially that provide an indication that they have failed.In step 930, if one or more sensors have failed, they are flagged instep 933, and the FLAG variable is set to one. If no sensors have beendetermined as failed, then processing continues at step 906.

Returning to step 906, t is now not equal to zero, having been set toone in step 908. The counter t is incremented in step 937, correspondingto a reading of the next snapshot of data from genuine sensors. Uponchecking the state of FLAG in step 940, if FLAG is still zero (no sensorhas failed since the last loop through the process), then D_(in) and Gremain the same in step 945, and the next snapshot is acquired andprocessed continuing with step 922 again. If, on the other hand, FLAGhas been set to one in step 933 as checked in step 940, then the arraysD_(in) and G must be recalculated in step 950. Rows are removed fromD_(in) corresponding to the failed sensors (these are not removed fromD_(out)). Array G is recalculated based on the new D_(in). The FLAG isreset to zero. Then, in step 922, as the snapshot of the monitoredprocess or machine is acquired, elements of the input vector Xcorresponding to the same failed sensors are removed. However, sinceD_(out) has not had any rows removed, the estimate of X generated instep 922 includes estimates for the missing rows, that is, failedsensors. These estimates are thus the virtual sensor values computed asreplacement values for the failed sensors.

Thus the embodiment advantageously provides the ability to generatereplacement signals on-the-fly for failed sensors in monitoring systemsemploying a similarity operation for computing estimates for comparisonto actual data. Such a replacement signal can be provided to downstreamprocessing that requires a sensor signal from the failed sensor(s).Accordingly, a complex sensor signal can be decomposed into multiplecorrelated inputs to provide an inferential measure of an uninstrumentedphysical parameter of a system.

Turning to FIG. 10, a hydraulic pump embodiment 100 is shown in which adiesel engine 102 drives a shaft 104 of the hydraulic system 100, whichactuates a piston 106 in a cylinder 108 for controlling the hydraulicsupply being provided by four-way directional valve 110. In thedescribed embodiment, an eight-step cycle is provided for the hydraulicsystem to facilitate variable flow rates. The system 100 is outfittedwith an accelerometer 112, preferably located so as to observevibrations longitudinal with the variable displacements of the pumpcylinders associated with the pistons 106 reciprocating therein. Theintroduction of contaminants in the hydraulic loop, such as particlesand metallic grains or the like, wear on the valve and piston of thesystem, causing changes in the hydraulic pressure. This results inchanges in vibrations from the pump, as it may compensate for the lossof pressure.

The parameter desirably estimated with a virtual signal in connectionwith the hydraulic system 100 can be the pressure or flow provided bythe system. An invasive pressure transducer in the hydraulic line,however, can be obstructive and susceptible to failure. Accordingly, theaccelerometer 112 is desirably used instead to facilitate virtualpressure readings correlated with the accelerometer 112. This isaccomplished by outputting the complex signal from accelerometer 112 toa power spectrum analyzer 114, which can be embodied in a computerrunning a software module, with a data acquisition device attached tothe accelerometer 112. The power spectral density (PSD) output by theanalyzer 114 provides the power of the accelerometer-measured vibrationas a function of the frequency of that vibration, using a 1024 samplefast Fourier transform (FFT) sliding window providing for frequency binswhich may be user selectable, e.g., 30 frequency bins over the powerspectrum being provided as an input observation vector for thesimilarity calculations as discussed above. Accordingly, the frequencycomponents associated with the user selectable bins provide multipleinput observations. The PSD can be used as a multi-variable input to theinferential signal generator. The uninstrumented physical parameter ofhydraulic pressure, or flow as desired, is the inferred signal. Theinputs from the PSD are the actual signals. These inputs can be selectedfrom the following several alternatives.

In the first alternative, selected frequencies only can be used asinputs. For example, with some knowledge of the vibration frequencieslikely to be of interest in the hydraulic system 100, severalfrequencies can be selected, and the value of the power at each of thesefrequencies can be used as a “sensor” input.

In another alternative, the frequencies can be “binned” or talliedacross several bands of frequencies. In this case, the value (or“sensor” signal) for a given band or bin of frequencies can be one ofthe highest power value in the bin, the lowest power value in the bin,the average power value across the bin, or the median power value in thebin. Other variations clearly would also work, and are within the scopeand spirit of the invention.

Thus, the described embodiments provide the benefit of working withdecomposed complex signals as input to inferring an uninstrumentedphysical parameter. In an exemplary embodiment, data was collected froma standard window-mounted room air conditioner operating over a varietyof expected conditions, in a large room serving as a thermal sink. Theoutputs from a total of 23 sensors were used and representedmeasurements of the temperature gradients across the evaporator andcondenser. The data were acquired from k-type thermocouples that weredigitized using a data acquisition board (DAQ) with a sampling ratesetting of 100 samples/sec. The data were collected while the airconditioner maintained the room environment at a relatively constanttemperature. The data was distilled to a training set according to themethods described herein. A large number of training snapshots (92, fourtimes the number of sensor variables) relative to the number of sensorswere employed to develop the empirical model of the air conditioner inoperation.

To measure the fidelity of the empirical model, a total of 600 randomlychosen operating observations were estimated using the model developedfrom the training. For each such observation, a snapshot of the full 23sensors was input to the model, which then generated an output of 23estimates for those same sensors. A reference modeling estimation errorwas defined as the ratio of the average root-mean-square (RMS) of theresidual (difference between the estimated and actual sensor value) tothe standard deviation of the noise on the actual sensor value. When all23 sensors were available as model input, the average estimation errorwas 0.271. This is a fraction of the average noise on the sensors.

The efficacy of accurately rendering virtual sensor signals is accessedby one after another sensor being randomly selected with value a set tozero, simulating sensor failures. A maximum of 12 sensors was failed,corresponding to a loss of 52% of the originally available sensors.Estimation error as described above is shown in the following table foran increasing number of failed sensors as an average across all sensors.As would be expected, the estimation error increased as the number offailed sensors increased. However, it is notable that the estimationerror across all the sensors remains comparatively low, indicating thatthe sensor estimates both for sensors that were not “failed” and evenfor sensors that were “failed” were usefully accurate.

Number of Average RMS of Failed Sensors Estimation Error 0 0.2706 10.2763 2 0.2915 3 0.3096 4 0.3141 5 0.3237 6 0.3402 7 0.3523 8 0.3791 90.4014 10 0.4095 11 0.4348 12 0.4649

Turning to FIG. 11, a chart is shown of a virtual sensor signalgenerated for the air conditioner after failing the original sensor andtwo others, and excluding them as inputs to the empirical model. Alsoshown is the actual value of the original sensor. The absissca of thechart is time in minutes. The ordinate is the value of the sensor,atemperature. As can be seen, when the sensor is treated as failed (aswell as two others in the set of 23), and not provided to the empiricalmodel, the model nonetheless generates a viable and useable estimate ofthe sensor value, based on the other values provided as input.

It will be appreciated by those skilled in the art that modifications tothe foregoing preferred embodiments may be made in various aspects. Thepresent invention is set forth with particularity in the appendedclaims. It is deemed that the spirit and the scope of that inventionencompasses such modifications and alterations to the preferredembodiment as would be apparent to one of ordinary skill in the art andfamiliar with the teachings of the present application.

What is claimed is:
 1. A system for monitoring operational equipment,comprising: a sensor capable of being mounted on the equipment foroutputting a complex signal comprising component signals; a signaldecomposing acquisition front-end coupled with said sensor for providinga plurality of component signals derived from said sensor; and aninformation processor operable in response to said sensor for using theplurality of component signals and one or more of the process parameterswith a relationship observed between the plurality of component signalsand an instrumented physical parameter of the equipment to generate aparametric signal corresponding to the uninstrumented physicalparameters.
 2. A system as recited in claim 1, comprising a plurality ofsensors.
 3. A system as recited in claim 2, wherein said informationprocessor uses a similarity operator to obtain a similarity measurebetween the plurality of component signals and one or more of theprocess parameters of the operational equipment for decomposing thecomplex signal into correlated component signals to provide anuninstrumented physical parameter.
 4. A system as recited in claim 1,wherein said information processor estimates the parametric signalcorresponding to one of the process parameters.
 5. A system as recitedin claim 2, wherein said information processor estimates the parametricsignal corresponding to a process parameter being monitored by one ofsaid plurality of sensors.
 6. A system as recited in claim 2, whereinsaid information processor determines a data acquisition failureassociated with said sensor such that said data acquisition front-end isinhibited from providing the component signals from said sensor to saidinformation processor, and wherein said information processor estimatesthe parametric signal corresponding to the component signals from saidsensor in response to the data acquisition failure.
 7. A system asrecited in claim 5, wherein the data acquisition failure corresponds toa failure of said sensor, and said information processor determines thefailure of said sensor.
 8. A system as recited in claim 5, wherein thecomponent signals from said sensor comprise a process parameter.
 9. Asystem as recited in claim 1, wherein the one or more process parametersof the equipment correspond to physical operating characteristicsincluding temperature, pressure, or displacement of the operationalequipment being monitored.
 10. An inferential signal generator,comprising: a memory for storing a set of time-correlated sensor datarepresentative of expected operational states of a system selected froma process or a machine; a signal acquisition input for receiving sensorvalues from said system while in operation, descriptive of physicalparameters of said system; a processor disposed to receive the sensorvalues from said signal acquisition input, and generate at least oneoutput value descriptive of a parameter of the system that is not amongparameters measured by the received sensor values, by comparing thesimilarity of the sensor values from said signal acquisition input tothe set of sensor data in said memory.
 11. An inferential signalgenerator as recited in claim 9, wherein said processor generates the atleast one output value by a linear combination of the set of sensordata, adjusted according to said similarity of the sensor values to saidset of sensor data.
 12. An inferential signal generator as recited inclaim 10, wherein the similarity of the sensor values from said signalacquisition input to the set of sensor data in said memory is measuredby an element by element comparison of a numerical closeness of likesensor values with a full range of values for like sensors in saidmemory.
 13. An inferential signal generator as recited in claim 10,wherein the set of sensory data in said memory comprises a plurality ofsnapshots of sensor data, each such snapshot comprising time-correlatedvalues from the sensors on the system.
 14. An inferential signalgenerator as recited in claim 12, wherein the sensor values received bysaid signal acquisition input from said system while in operationcomprise a snapshot of time-correlated values from a subset of thesensors on the system.
 15. An inferential signal generator as recited inclaim 13, wherein said processor generates the at least one output valueby a linear combination of the plurality of snapshots in said memory,adjusted according to said similarity of each such snapshot to thesnapshot received by said signal acquisition input.
 16. An inferentialsignal generator as recited in claim 9, wherein said signal acquisitioninput comprises a data bus electrically connected to sensors of saidsystem.
 17. An inferential signal generator as recited in claim 9,wherein said signal acquisition input comprises a wirelesscommunications link disposed to receive transmissions containing thesensor values.
 18. A control apparatus for a system selected from aprocess or machine, comprising: at least one actuator signal lineconnected to said system for conducting a control signal to said system;at least one sensor signal line connected to said system for conductinga signal from at least one sensor on said system indicative of aphysical parameter of said system; a memory for storing a set oftime-correlated sensor data representative of expected operationalstates of said system; and a processor disposed to receive the signalfrom the at least one sensor signal line, for generating a controlsignal provided to said actuator signal line, by comparing thesimilarity of the signal from said sensor signal line to the set ofsensor data in said memory to generate at least one computed valuedescriptive of an physical parameter of said system, on the basis ofwhich said control signal is generated.
 19. A control apparatus asrecited in claim 17, wherein said processor generates the at least onecomputed value from a combination of the set of sensor data, adjustedaccording to said similarity of the sensor signal to said set of sensordata.
 20. A control apparatus as recited in claim 18, wherein saidsimilarity is measured by a numerical closeness of the sensor signalfrom said at least one sensor signal line to like sensor data in saidmemory.
 21. A method for generating at least one inferential sensorsignal for a system selected from a machine or process, comprising thesteps of: instrumenting said system with a first set of sensors and asecond set of sensors to measure a plurality of physical parameters ofsaid system; operating said system in at least one operational state;acquiring sensor data from said first set of sensors and said second setof sensors for the plurality of physical parameters for the at least oneoperational state to provide an inferential measure of an uninstrumentedphysical parameter not among paramaters measured with respect to saidsecond set of sensors; storing the acquired sensor data from said firstset of sensors and said second set of sensors in a memory; monitoringvalues of said first set of sensors while said system is in operation;and computing at least one inferential sensor signal from said secondset of sensor signals corresponding to a physical parameter not amongthose measured by said first set of sensors, by linearly combining thestored sensor data according to a measure of similarity of the monitoredsensor values to the stored sensor data.
 22. A method according to claim20, wherein said measure of similarity is an element-by-elementcomparison of a numerical closeness of values of the monitored sensorvalues to values of like sensors in the stored sensor data.
 23. Acomputer for generating virtual sensor signals describing a physicalsystem, comprising: a memory for storing a plurality of reference statevectors, each state vector having as elements sensor values descriptiveof a physical state of said system; a first computing module disposed toreceive a current state vector describing said physical system, havingas elements sensor values corresponding to a subset of sensors in eachof said reference state vectors, for comparing the current state vectorto each said reference state vector to determine a measure of similaritytherebetween; and a second computing module disposed to receive themeasures of similarity between the current state vector and each saidreference state vector, and generate from a combination of saidreference state vectors as weighted by the measures of similarity, avirtual signal vector having as elements estimates of those sensorvalues corresponding to sensors in said reference state vectorsremaining out of said subset of sensors.
 24. A computer as recited inclaim 23, wherein said second computing module generates at least oneoutput value descriptive of a parameter of the physical system toprovide a virtual signal in addition to the sensor values correspondingto the subset of sensors of said reference state vectors.
 25. A computeras recited in claim 24, wherein said second computing module generatesthe virtual signal as a linear combination of said reference statevectors adjusted according to the measure of similarity of saidreference state vectors to observed sensor data